# DE and vector question (1 Viewer)

#### kractus

##### Member

How would you do these?

#### jimmysmith560

##### Le Phénix Trilingue
Moderator
Would the following working help for the first question?

$\bg_white \Rightarrow \frac{R_{A}}{R_{B}}= \frac{\left ( T_{tA}-T_{s} \right )}{\left ( T_{tB}-T_{s} \right )}$

$\bg_white \Rightarrow \frac{R_{A}}{R_{B}}= \frac{\left ( T_{tA}-T_{s} \right )}{\left ( T_{tB}-T_{s} \right )}$

$\bg_white \Rightarrow \frac{R_{A}}{R_{B}}= \frac{\left ( 120-40 \right )}{\left ( 80-40 \right )}$

$\bg_white \Rightarrow \frac{R_{A}}{R_{B}}= \frac{2}{1} \ \text{i.e. (B).}$

#### kractus

##### Member
Thanks it helped. What about the other question? I'm still kinda confused lol

#### jimmysmith560

##### Le Phénix Trilingue
Moderator
Thanks it helped. What about the other question? I'm still kinda confused lol
No worries. Would the following help with the other question?

$\bg_white x'(t)=\frac{-1}{\sqrt{1-t^2}}$

$\bg_white y'\left(t\right)=\frac{1}{\sqrt{1-t^2}}$

$\bg_white \text{Distance}=\int _{-1}^1\sqrt{\left(\frac{-1}{\sqrt{1-t^2}}\right)^2+\left(\frac{-1}{\sqrt{1-t^2}}\right)^2}dt$

$\bg_white =\sqrt{2}\int _{-1}^1\frac{1}{\sqrt{1-t^2}}\ dt=\sqrt{2}\pi \: \ \text{i.e. (D).}$